Problem: Express this product in scientific notation: $(6.10\times 10^{3})\times (5.00\times 10^{1})$
Solution: Start by collecting like terms together. $= (6.10\times 5.00) \times (10^{3}\times 10^{1})$ When multiplying exponents with the same base, add the powers together. $= 30.5 \times 10^{3\,+\,1}$ $= 30.5 \times 10^{4}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the left without changing the value of our answer. $ $ We can use the fact that $30.5$ is the same as $3.050 \times 10$ $ = {3.050 \times 10} \times 10^{4} $ $= 3.050\times 10^{5}$